What's the difference between "the church" and "Christianity"?
Christianity was first known as "The Way." It was not even established as the "Christian Religion" until much later. The first groups of people who followed "The Way" were Jews who saw that Christ was the promised Messiah and Savior of the world. They saw following The Way as a continuation of Judaism rather than as a separate religion called Christianity.
Judaism and Christianity are moral and philosophical constructs given to us by God in order for us to seek and find Him, and to obtain the original goal of mankind which was lost in the Garden of Eden. As we follow those teachings, which were first given to us by in the Law of the Old Covenant and then perfected and fulfilled in Christ, we are changed from beings who easily follow sin to beings who begin to love God and love others. The Law of God was reduced to two great commandments, which are the heart of all that we do - love God supremely, and love your neighbor as yourself. God is love and as we become beings of love by our union with Him, we become like Him. That is the goal.
The Church is the family of God. If you read the Bible, you will notice there is much familial language in it. God is our Father. The Blessed Virgin is our Mother. Jesus is the Elder Brother (the Covenant First-Born and Head of Covenant). We are called brothers and sisters (but unfortunately we don't always treat each other with such familial care).
The Church is the place where God establishes that worship which has a distinct purpose: that it shows through symbols the invisible Kingdom of God.
Heb 8:5 Who serve unto the
example and shadow of heavenly things, as Moses was admonished of God when he was about to make the tabernacle: for, See, saith he,
that thou make all things according to the pattern shewed to thee in the mount.
Heb 9:23 It was therefore necessary that the
patterns of things in the heavens should be purified with these; but the heavenly things themselves with better sacrifices than these.
When God established the Church in the Old Covenant, He gave to Moses specific instructions on how to build the tabernacle, the priesthood, and the laws regulating worship, and was we see in Heb. 8:5, He warned mankind not to tamper with those things by introducing man-made ideas. This carries over into the New Covenant where each Divine Liturgy is a picture - a symbol and type - of heavenly things.
The Church is also the body which carries out the authority of God on earth. It establishes proper worship and defines what is truth and what is heresy. Without that, mankind is left bereft of instruction and creates his own God, His own Jesus, and his own worship. The multitude of various different "worship" forms is a mute testimony to this truth. You have everything from the Jimmy Swaggart Jesus Jazz Cafe to the High Anglican Liturgy and all forms in between, each calling themselves "worship." This is what man does without the guidance of the Church which Christ established on earth.
So Christianity is The Way....the way we seek God and find Him. It is the principles of the life of a God-seeker. The Church is the authority which aids men and women in eschewing that which is false, finding that which is true, disciplining the family of God, and gathering together for worship.
I hope that helps a bit. Perhaps someone else can add to it.